Gene Network Modeling

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Gene Network Modeling

• Daniel Zak
• Department of Chemical Engineering, UD
• Daniel Baugh Institute, TJU
• zak_at_che.udel.edu
• February 1, 2001

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Outline

• Gene network examples
• Modeling issues and challenges
• Opportunities with DNA microarray data

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Gene network examples

• Ribosomal proteins
• Lysis/lysogeny circuit
• Circadian rhythms
• Yeast cell cycle
• Yeast diauxic shift
• CNS development
• Human fibroblast response to serum

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Ribosomal Protein Negative Feedback
Lewin, 1999, Genes VII, p.304, (http//www.ergito.
com/docs/start.htm)
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l-phage Lysis/Lysogeny circuit
http//esg-www.mit.edu8001/esgbio/pge/pgeother.ht
ml
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Circadian rhythms (Tyson et al., 1999)
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Yeast Cell Cycle (Chen et al., 2000)
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Yeast Cell Cycle (Spellman et al., 1998)
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Yeast Diauxic Shift (DeRisi et al., 1997)
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CNS Development (Wen et al., 1998)
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Fibroblast Serum Response (Iyer et al. 1999)
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Gene network modeling

• Why model?
• Interconnections too numerous and complex for
  intuition
• Modeling issues
• Scale (40,000 genes in human genome)
• Nonlinearities
• Multistability
• Oscillations
• Delays
• Small numbers of molecules

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Multiple Binding Site Activator (Keller, 1994)
Steady state rate of synthesis rate of decay
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Multiple Binding Site Activator (Keller, 1994)
c 1, e 0.04, Q 0.001, n 0.1, K1 K2 0.5
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Multiple Binding Site Activator (Keller, 1994)
c 1, e 0.04, Q 0.001, n 0.1, K1 K2 0.5
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l-phage Lysis/Lysogeny circuit

• Multistability may play a role in development and
  adaptation
• Shows mathematically how a single genotype can
  give rise to multiple phenotypes

http//esg-www.mit.edu8001/esgbio/pge/pgeother.ht
ml
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Genetic Switch (Cherry and Adler, 2000)
Steady state dX/dt dY/dt 0 Multiple
steady states possible for n gt 1 (cooperativity)
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Genetic Switch (Cherry and Alder, 2000)
time, s
k1 0.2, k2 1, m1 m2 0.05, n 2
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Circadian Rhythms (Tyson et al., 1999)
nm 1, km 0.1, vp 0.5, kp1 10, kp2
0.03 kp3 0.1, Keq 200, Pc 0.1, Jp 0.05
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Circadian Rhythms (Tyson et al., 1999)
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Delays

• Transport (Smolen et al., 2000)
• Active
• Evidence for active transport of mRNA (Femino et
  al,, 1998)
• Modeled with a discrete delay, X( t - t )
• Can destabilize steady states
• Passive
• Evidence for passive transport of mRNA (Femino et
  al., 1998)
• Modeled with diffusion equations
• Tends to damp oscillations
• Cellular processes
• Transcription (minutes)
• Translation (hours)
• Post-translational modifications (minutes -
  hours)
• Modeled with discrete delays or rate laws

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Time delay (Scheper et al., 1999)
rM 1, rP 1 qM 0.21, qP 0.21 n 2, m
3 t 4, k 1
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Time Delay (Scheper et al., 1999)
mRNA vs Protein
Protein vs time
t 0 hr
t 0 hr
t 2.2 hr
t 2.2 hr
t 4 hr
t 4 hr
time, hr
Protein
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Small numbers

• Many intracellular factors are present in small
  numbers (McAdams and Arkin, 1999)
• mRNAs, transcription factors, signaling
  molecules
• Conventional formalism for chemical kinetics
  breaks down
• r ? kXnYm
• rmean kXnYm
• Microscopic fluctuations in rates can have
  macroscopic consequences
• Combustion
• Gene networks

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Stochastic formulation (Gillespie, 1976)

• Assumptions
• Well-mixed environment (no geometry)
• P(reaction i , t) a rmacro(t)
• Monte Carlo approach
• generate Dt randomly from weighted distribution
• pick reaction i randomly from weighted
  distribution
• Applications
• Transcription/Translation (Kierzek et al., 2000)
• Lysis/Lysogeny Circuit (Arkin et al., 1998)
• Circadian rhythms (Barkai and Leibler, 2000)

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Protein vs. time (Scheper et al., Tyson et al.)
N 100
N 1000
N 10000
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Protein Period vs N with Fluctuations
Tyson et al.
Scheper et al.
N
N
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Challenges with Stochastic Approach

• Are cells well-mixed?
• Are macroscopic rate laws relevant to stochastic
  processes?
• Complications from active transport and
  localization?
• How to include spatial effects?

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DNA Microarrays

• DNA microarrays (RT-PCR, Oligos, cDNA, SAGE)
• relative transcription levels for thousand of
  genes in parallel
• correlate transcription levels to any phenotypic
  state
• transcription levels during phenotypic change may
  elucidate genetic circuitry
• Challenges with microarray data
• normalization
• standards
• assessing quantitative value
• Successful applications in class distinction (eg.
  Leukemia class, Golub et al., 1999)
• Several approaches for elucidating networks from
  temporal microarray data have been developed

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CNS Development (Wen et al., 1998)
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Fibroblast Serum Response (Iyer et al. 1999)
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DNA Microarrays

• Challenges in elucidating networks from temporal
  microarray data
• Curse of dimensionality
• 1,000 genes, 10 time points ? 104 equations, 106
  unknowns!!
• Lack of control over inputs
• Causality
• Some approaches
• Cluster genes by expression profile similarity,
  then elucidate network between clusters
• Boolean genes are on or off (Kauffman, 1994)
• Continuous
• Linear (Dhaeseleer et al., 1999 Someren et al.,
  2000)
• Linear squashing (Weaver et al., 1999)
• Differential (Chen et al., 1999)

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Continuous Approaches

• Linear Successful prediction, limited inference
  (Wessels et al., 2001)
• Linear plus squashing
• Differential Requires initial protein levels

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Big Challenges

• Tens of thousands of cell types...
• Tens of thousands of genes...
• Tens of thousands of protein states...
• Nonlinearities...
• Spatial effects...
• Transport effects...
• Stochastic effects
• Limited data (this is changing)
• What would Jake and Elwood do?

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